Hertzian dipole: if the charge on the first spherical conductor is Q, why the other conductor has a charge -Q

I've read that "the system has zero net charge", but what's the reason for this?

With no applied voltage, both spheres are neutral - each contains the same number of negative charges (electrons) and positive charges (protons, in the atomic nuclei).

Only some of the electrons are mobile (free to move); they are called the conduction electrons.
(Most of the electron and the all of the nuclei are fixed because of the interatomic forces holding the atoms together in the lattice.)

When a voltage is applied, one sphere is made positive because electrons are removed from it. The other sphere is made negative because electrons are added to its. The applied voltage causes a flow of the conduction electrons from one sphere to another, making one positive and the other negative.

Changing the polarity reverse this.

The net charge remains zero because the total number of electrons and the total number of protons are equal and neither changes - it's just that some of the electrons have moved from one side to the other.

It's just the same a charging a capacitor - one plate becomes positive and the other negative.

In simple terms...it is conservation of charge...like we have conservation of energy